Continuum mechanics has been used for simulating continuous matter such as solids and fluids (i.e., liquids and gases). Differential equations are employed in solving problems in continuum mechanics. Many numerical procedures have been used. One of the most popular methods is finite element analysis (FEA), which is a computerized method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are referred to as finite elements. The vertices of the finite elements are referred to as nodes. The model is comprised of a finite number of finite elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment is created.
One of the most challenging FEA tasks is to simulate an impact event such as car crash. As the modern computer improves, not only are the vehicle behaviors in a car crash simulated, but also the occupant's movements and reactions. In order to adequately simulating an occupant (i.e., a human), movements according to bio-mechanical properties of a human body (e.g., muscles) need to be model properly in the CAE (e.g., finite element analysis). As of today, there is no satisfactory practical solution. Some of the prior art approaches cause unsmooth or jerky movements due to traditional finite element method, for example, truss element that maintains its original length throughout the simulation. It would therefore be desirable to have method and system for numerically simulating muscle movements along bones and around joints.